Average Error: 0.0 → 0.0
Time: 12.0s
Precision: 64
\[0 \le x \le 2\]
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[\left(1 + x\right) \cdot \left(x \cdot x\right)\]
x \cdot \left(x \cdot x\right) + x \cdot x
↓
\left(1 + x\right) \cdot \left(x \cdot x\right)
double f(double x) {
        double r2861281 = x;
        double r2861282 = r2861281 * r2861281;
        double r2861283 = r2861281 * r2861282;
        double r2861284 = r2861283 + r2861282;
        return r2861284;
}
↓
double f(double x) {
        double r2861285 = 1.0;
        double r2861286 = x;
        double r2861287 = r2861285 + r2861286;
        double r2861288 = r2861286 * r2861286;
        double r2861289 = r2861287 * r2861288;
        return r2861289;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[\left(\left(1.0 + x\right) \cdot x\right) \cdot x\]

Derivation

  1. Initial program 0.0

    \[x \cdot \left(x \cdot x\right) + x \cdot x\]
  2. Using strategy rm

  3. Applied distribute-lft1-in0.0

    \[\leadsto \color{blue}{\left(x + 1\right) \cdot \left(x \cdot x\right)}\]

  4. Final simplification0.0

    \[\leadsto \left(1 + x\right) \cdot \left(x \cdot x\right)\]

Reproduce

herbie shell --seed 2019151 
(FPCore (x)
  :name "Expression 3, p15"
  :pre (<= 0 x 2)

  :herbie-target
  (* (* (+ 1.0 x) x) x)

  (+ (* x (* x x)) (* x x)))